The next number is 12.
The rule is
Un = (2n4 - 27n3 + 123n2 - 214n + 120)/2 for n = 1, 2, 3, ...
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10, 8, 6, 4, 2, 0, -2, -4
16
64
The Fibonacci sequence. The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The next number is found by adding up the two numbers before it
The next number is 1. The simplest polynomial rule is Un = (-15n4 + 202n3 - 921n2 + 1646n - 888)/24 for n = 1, 2, 3, ...